For a general linear inverse problem, [1]}, [2]} proposed to apply AMP to a unitary transform of the original model,
where blackthe unitary matrix for the transformation can be obtained by the singular value decomposition (SVD) of \(\mathbf {A}\) . In the case of a circulant \(\mathbf {A}\) , blackthe normalized discrete Fourier transform matrix can be used for the unitary transformation, enabling highly efficient implementation with the fast Fourier transform (FFT) algorithm [3]}.
This leads to an AMP variant named unitary AMP (UAMP), which was formerly called AMP with unitary transformation (UTAMP). blackSVD plays an important role in both UAMP and VAMP. In UAMP, SVD is used to obtain the unitary transformed model. In VAMP, the linear minimum mean squared error (LMMSE) estimator results in cubic complexity in each iteration, and VAMP relies on SVD to implement the LMMSE estimator with low complexity.
blackIn this work, we apply this concept to SBL, resulting in a new SBL algorithm called UAMP-SBL. UAMP-SBL achieves more efficient sparse signal recovery with significantly enhanced robustness, compared to the state-of-the-art AMP-based SBL algorithm GGAMP-SBL [4]}.
